Once you install the application a code script is loaded on your store. This script loads either through the Script tags API or through the App extensions. This selection depends on the way you have selected the initial screen of the app.
Script tag API
If this installation method is selected then the app loads on the store regardless of the theme that is being used and even if you decide to switch your theme, then the application will still work on the new theme without any changes needed.
If this installation method is selected then the app loads as an app embed and this is configured from your Theme Settings page. This means that if you switch store theme, you will need to visit the new theme settings page to enable again this app extension.